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Why is the distance between two lines only defined for parallel lines?
Wiki User
∙ 10y ago
because they never intersect
Wiki User
∙ 10y ago
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How do you find the shortest distance between two parallel lines?
The shortest distance between 2 parallel lines is a perpendicular drawn between 2 parallel lines the diagram shows it clearly 1 parallel line ------------------------------------|-------------------------------------------------------------------- | | | the vertical line is the shortest distance | | ------------------------------------|------------------------------------------------------------------- 2nd parallel line
Are railway lines parallel or perpendicular?
Railway lines are parallel. 2 lines are said to be parallel when they are contained in the same plane and do not intersect. This is the definition. That parallel lines exist is an assumption (postulate) of Euclidean geometry:Parallel lines are like the rails of a train track, and you might think of defining them this way, as lines that are the same distance apart everywhere. The problem with this kind of definition is it assumes both tracks are straight. Though this seems an obvious possibility, when you go into the vast universe it is not that obvious. Parallel lines puzzled the best mathematicians for centuries until it was realized that we must assume they exist (you can't prove they exist from simpler postulates). The problem with parallel lines lies in the notion that the lines have infinite extent.Euclid used a somewhat different parallel postulate in trying to avoid the notion of the infinite. He observed that when two parallel lines are intersected by a third line, called a transversal, then if you measure two angles formed by these three lines, on the same side of the transversal and between the parallels, they will add to (that is, they will be supplementary). Such angles are called same-side interior angles.Another important concept is perpendicular. By definition, two lines are perpendicular if they intersect at right angles. That is, two perpendicular lines form 4 right angles. Segments and rays can also be perpendicular. This means they intersect in at least one point, and the two lines containing them are perpendicular.We use perpendicular segments to measure the distance from a point to a line, a point to a plane, or the distance between two parallel lines or planes. The ties of a railroad track are perpendicular to the rails and of the same length. This common length is the distance between the rails. (If parallel lines exist, then railroad tracks in space can go on forever.)There are three theorems about perpendicular lines that you should know. We will not attempt to prove them here, but if you think about them they should be rather obvious.We can use this fact to define the distance from a point to a line: That distance is the length of a segment perpendicular to the line with the given point as one of its endpoints and the other endpoint on the line. In fact, a similar notion holds in 3 dimensions. If we have a plane and a point not on that plane, then there is only one line through the point perpendicular to the plane, and the length of the segment determined by that point and the intersection of the perpendicular line with the plane is defined as the distance from the point to.
How would you know if lines a perpendicular or parallel?
perpendicular lines intersect each other at 90 degrees whereas parallel lines never intersect each other and remain equal distance apart from each other. Obviously the way to test if two lines are parallel is to measure their distance from each other at at least two points (the farther apart the better) to confirm that they remain equal distance apart, but to test if lines are perpendicular, with a compass with the point at the point where the two lines intersect, draw an arc (or three parts of an arc) that intersects one of the lines in two places and the other line in one place. If the distances between the lines at the points where they are intersected by the arc are equal, the lines are perpendicular.
Does a parallel lines intersect?
No never because they remain equal distance from one another
If two lines are parallel do they have the same slope?
Yes but they remain equal distance apart from each other
How do you find out if lines are parallel?
If the distance between the lines is constant then they are parallel.
Name that line lines that always have the same distance between them?
parallel lines - they are parallel when the distance between them remains constant
Does perpendicular lines have a constant distance between them?
No but parallel lines have a constant distance between them
How do you find the shortest distance between two parallel lines?
The shortest distance between 2 parallel lines is a perpendicular drawn between 2 parallel lines the diagram shows it clearly 1 parallel line ------------------------------------|-------------------------------------------------------------------- | | | the vertical line is the shortest distance | | ------------------------------------|------------------------------------------------------------------- 2nd parallel line
What is the Minimum distance between parallel lines?
Can be as little as you like.
What line passes through 2 parallel lines?
Any line that is not parallel to the given lines. The transversal that contains the shortest distance between the two parallel lines, is perpendicular to them.
What no sides are parallel?
the lines which have equal distance between them throuhout the stretch
Is the distance between the two parallels is not same?
The perpendicular distance between two parallel lines is always the same.
Why is parallel lines defined?
Otherwise nobody would know what was meant by parallel lines!
What is defined as the convergence of lines in the distance?
A vanishing point is defined as a convergence of lines in the distance.
Can intersecting lines also be parellel?
No, parallel lines are defined as always being the same distance away from each other, or having the same slope.
What are two characteristics of parallel lines?
They never meet, and the distance between them stays the same
